Posts Tagged ‘exponents’
Thursday, November 12th, 2009
How to Solve Negative Exponents
Description
A detailed tutorial on how to solve negative exponents. Step by step tutorial including several examples of solving negative exponents for reference.
Overview
An exponent is a number representing how many times you multiply the base – the number the exponent is on – by itself. Which is why negative exponents are so confusing – how can you multiply something by itself a negative number of times? The easiest way to think of a negative exponent, is that if you take away the negative sign and put the base and exponent under the number 1 (like as a fraction), you are saying the same thing! A negative exponent simply needs to be moved to the denominator (or the numerator, if it is in the denominator) to make it a positive exponent. This can be tricky when there are other numbers or expressions found in the same fraction, but not impossible.
Tags: algebra, base, denominator, equation, exponents, expression, fraction, multiply, negative, numerator, positive, power
Posted in Algebra | No Comments »
Thursday, November 5th, 2009
Definition of an Operand
Description
A detailed tutorial on the definition of an operand. Step by step tutorial including several examples of an operand for reference.
Overview
An operand can be any number. However, a number is only called an operand when there is some kind of operation being performed on it. There are simple operands and complex operands. A simple operand is what people call an operand – just one number. A complex operand is an operand that consists of an operation inside it, and therefore has at least 2 operands inside the first operand.
Tags: addition, arithmetic, complex, division, exponents, multiplication, number, operand, operation, order, parenthesis, simple, subtraction
Posted in Arithmetic | No Comments »
Thursday, September 10th, 2009
How to Solve a Fractional Exponent
Description
This video shows two different ways of solving fractional exponents and explains what to do if the exponents are negative as well as fractional. Several example problems are scattered throughout the video to make learning easier.
Overview
All of you are probably familiar with exponents by now, but what do you do if the exponent is a fraction? What a fractional exponent is, is a square root, cube root, or any other root function. The number in the denominator is your root function, and the number in the numerator is the power you are raising it to. For example, if you have a 3/2 power, then you have the square root of 4 to the third power. While roots, also called radical functions, can be confusing, often it is a great improvement from the fractional exponent you had previously. If for some reason you need a fractional exponent, this process also works in reverse – radical functions can be changed into exponents. Normally there is no need to do that until calculus, but it is good to know anyway.
Tags: algebra, exponents, fractional exponents, fractions, Math, negative, negative exponents, positive, radicals, roots, to the power
Posted in Algebra | No Comments »
Friday, September 4th, 2009
How to Solve Derivatives with Logarithmic Functions
Description
This video covers the basic exponential and logarithmic functions, and then shows several sample problems. Many example problems of solving for natural logs are provided in the video. This video also shows the relationship between exponents and natural logs.
Overview
Derivatives with logarithms are rather easy to solve. The first of these is the regular exponent. The exponent is an exponential function, not a logarithmic function, but the two are related. The solution for an exponent, e^x, is:
d/dx (e^x) = e^x
Remember that the exponential solution only works when the variable x is the exponent, and to not use this when you should be using the power rule. The two look very similar and it is easy to mix them up. A problem using the power rule looks like x^2. A problem using the exponential rule looks like 2^x.
The next of these is a natural log. A natural log is a logarithm in its natural form. It is not necessary to understand natural logs to solve a derivative problem with natural logs. This should be a derivative that you have memorized. The natural log is solved like this:
d/dx [ln(x)] = 1 / x
In other words, to solve a natural log simply put one over whatever is inside the parenthesis. Remember that it may be necessary to use other rules with this rule.
Tags: Calculus, derivative, derivatives, differentiation, exponential, exponents, logarithmic, logarithms, logs, Math, natural logarithms, natural logs
Posted in Calculus | No Comments »
Thursday, September 3rd, 2009
An Introduction to Logarithms
Description
This video begins with the basics of logarithms and how they relate to exponents, showing examples of the same problem in both an exponent and a logarithm. It goes onto explain how to solve different types of logarithms, even going a little bit into scientific notation. Easy step-by-step instructions can be found in this video.
Overview
Many things in math have a reverse, and logarithms are no different. The opposite of a logarithm is an exponent, something most people are familiar with. The concept of logarithms, often called logs, is a bit more complicated than an exponent, but just as easy to learn.
Logarithms use “sub” values as well as exponential values. Sub values are values that are written a little bit lower than the number, as opposed to the “little bit higher” that exponential values are placed. They also have a slightly different meaning, although that meaning is not strictly important in a log.
Example: x^y = z, therefore {log(sub)x}^z = y
Number Example: 4^2 = 16, therefore {log(sub)4}^16 = 2
As is visible in the examples, the goal of a logarithm function is to find the exponent. The logarithm is basically asking you: “This number to (what power?) is equal to this other number.”
Tags: algebra, exponential equations, exponents, logarithmic equations, logarithms, logs, Math
Posted in Algebra | No Comments »
Thursday, September 3rd, 2009
How to Use Scientific Notation
Description
This video explains each part of scientific notation and lays it out in an easy to read format. It explains the basic concept of exponents and what multiplication by 10 does to a number, then moves onto how to solve scientific notation and how to convert regular numbers into scientific notation. Many examples are provided.
Overview
Scientific notation is a shorthand for very big and very small numbers. It consists of a number multiplied by 10 to the nth power. This power is very often a small, positive number. You use scientific notation by moving the decimal over n number of spaces and filling in any empty spaces with the number zero. To convert a number into scientific notation, move the decimal point until you create a number that is less than 10 but bigger than 0. An easier way to remember it is leave only one number before your decimal point. The number of decimal points you moved over is the number you put as the exponent. An example is 2.468 * 10^8. Move the decimal point over 6 spaces. Your number is 246800000. Now take the number 4928400000. To convert this to scientific notation, we want to create the number 4.9284. We moved the decimal point 9 spaces to get that number, so in scientific notation it is 4.9284 * 10^9.
Tags: algebra, decimals, exponents, Math, multiplication, Science, scientific notation
Posted in Algebra | No Comments »
Friday, August 28th, 2009
Exponents Explained
Description
A detailed tutorial on how to solve different exponents. Step by step tutorial including several exponential problems for reference. Knowledge of exponents are a requirement for algebra.
Overview
Exponents follow a basic form of multiplication.
When solving an exponent, is important to not read it as multiplication, but “to the power”. Powers mean a number mulitiplied by itself, the number of times the power represents.
Example: 2^3 = 2 * 2 * 2 = 8, while 2 * 3 = 6. Multiplication and exponents are not the same.
Tags: algebra, arithmetic, exponential equations, exponents, Math, multiplication, powers, to the power
Posted in Algebra, Math | No Comments »
Friday, August 28th, 2009
Order of Operations Explained
Description
A detailed tutorial on the use of Order of Operations. Step by step tutorial including few examples for reference. Knowledge of the Order of Operations is important for basic arithmetic.
Overview
The order of operations is better known as PEMDAS: Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction. This means that you follow that order when solving a long equation, and if there is more than one set of a certain operation then you move in the order of left to right. You can use a mnemonic to remember PEMDAS. The most common one is Please Excuse My Dear Aunt Sally, but if you like you can be creative and come up with your own!
Tags: addition, arithmetic, division, exponents, Math, multiplcation, order of operations, parenthesis, subtraction
Posted in Arithmetic | No Comments »
